Alfred North Whitehead

Alfred North Whitehead's father, also named Alfred Whitehead, was an Anglican clergyman from Ramsgate. He is said to have been an upright man with countless friends and Alfred North Whitehead's son, North Whitehead, wrote of his grandfather:-

He never asked a favour of anyone and never shirked what he considered to be a duty, but it cannot be said that he spent more time absorbing the lessons of the New Testament than was necessitated by his calling.

Canon Alfred Whitehead, the mathematician's father, married Maria Sarah Buckmaster, who came from London, on 20 December 1851. She is described as (see [6]);-

... an unimaginative, small minded woman with some wit but no sense of humour.

Alfred and Maria Whitehead had four children, with Alfred North Whitehead as the youngest of the family. He had two brother who were seven and eight years older than he was, and a sister who was two years older. Whitehead was always treated by his parents as the baby of the family and, rather surprisingly, they considered him a sickly and frail child when it appears that this was not the case. Whitehead was not sent to primary school because his parents thought that he was too delicate, so he was taught at home by his father until he was 14. Other than the usual childhood illnesses he was, despite his parents views, a healthy child. He received much affection from his father and brothers (but sadly little from his mother) and he seems to have had a childhood which was not unhappy, even though he was on his own a great deal and must have been somewhat lonely.

Whitehead's father taught him Latin from the age of ten and Greek from the age of twelve. His ability in these subjects could certainly be classed as competent but it was certainly not outstanding; there was no sign of the genius that he showed later in life. He did learn a little mathematics from his father but quite how he developed an interest in the subject is a mystery. In September 1875 he left his father's vicarage and entered Sherbourne Independent School. His oldest brother became a teacher at the school in 1876 when Whitehead was entering his second year of study.

The course he followed at Sherbourne was a fairly standard one for the time. There was little choice of subjects and all the boys studied as their major subjects Latin, Greek and English, with the minor subjects of mathematics, physical sciences, history, geography and modern languages receiving less attention. Whitehead showed a special gift for mathematics and was allowed to devote extra time to that subject in his final school year, dropping composition and reading of Latin poetry to make way for the extra mathematics.

In 1879 Whitehead took the entrance examinations for Trinity College, Cambridge, and he won a scholarship. Following this he spent his final year at Sherbourne as Head Boy and Captain of Games before he entered university in October 1880. As the holder of a scholarship, Whitehead lived in College. He attended only mathematics lectures and was taught by J W L Glaisher, H M Taylor, and W D Niven. He also attended lectures by Stokes and Cayley while his coach was the famous E J Routh. Among his close friends at Cambridge was D'Arcy Thompson.

Whitehead won a second scholarship, a College Foundation, and so by the time he entered his second year of study he was quite well off. He took the Mathematical Tripos examinations in 1883 and was placed Fourth Wrangler; the Senior Wrangler that year was G B Mathews (the Senior Wrangler was ranked first, the Fourth Wrangler ranked fourth in the list of students awarded a First Class degree). In the following year he was also placed in the First Class of Part III of the Mathematical Tripos. He presented a dissertation on Maxwell's theory of electricity and magnetism in the competition for a Fellowship in 1884. Thomson and Forsyth were appointed to examine Whitehead and, much to his surprise, he won one of the five scholarships available that year.

After winning the Fellowship, Whitehead was appointed to an assistant lectureship. He taught mostly applied mathematics but, surprisingly, he published no papers during the first five years of his tenure of the Fellowship. It is not known if he worked on mathematical research over this period. Certainly he was very much of a loner and did not talk much with the other mathematicians. In the twelve years following taking up the teaching position at Cambridge he published only two papers, both in 1889 on the motion of viscous fluids. The reason that the topic interested him was almost certainly because he had attended lectures by Stokes on viscous fluids.

Despite his poor publication record, Whitehead was promoted to a Lectureship at Cambridge in 1888. He took up additional teaching duties by accepting a teaching position at Girton College. All the signs at this time would point to him having decided that his strength was in teaching and not in publishing. A rather remarkable change came, however, when he married Evelyn Wade in London on 16 December 1890 [6]:-

Whereas he was quiet and restrained, she was active and outgoing.

He had become interested in pure mathematics and he started work on Treatise on Universal Algebra in January 1891, just weeks after his marriage. The work would take him seven years to complete, not finally being published until 1898. Whitehead's wife, Evelyn Wade, was the daughter of Captain A Wade, and they had three children, two sons and a daughter. The younger of the two sons, Eric Alfred Whitehead, became a second Lieutenant in the Royal Flying Corps (which was set up in 1912 and later became part of the Royal Air Force) and died while on a flying patrol in France in 1918.

Other changes in Whitehead's life took place around the time of his marriage. We have already indicated that Whitehead's father was an Anglican vicar and, of course, Whitehead was brought up as an Anglican. However around 1889-90 he began to move towards the Roman Catholic Church. He debated with himself for seven years whether to remain an Anglican or join the Roman Catholic Church. In the end he chose neither and became an agnostic around the mid 1890s. He himself stated that the biggest factor in his becoming an agnostic was the rapid developments in science; particularly his view that Newton's physics was false. It may seem surprising to many that the correctness of Newton's physics could be a major factor in deciding anyone's religious views. However one has to understand the complex person that Whitehead was, and in particular the interest which he was developing in philosophy and metaphysics.

We should return to the story of the Treatise on Universal Algebra which Whitehead worked on for much of the 1890s. Perhaps the first comment we should make is that the work is not on the modern topic of universal algebra for the term 'universal algebra' had quite a different meaning to Whitehead. In fact the name was taken from a paper published by Sylvester fourteen years earlier. In the Preface to the treatise he writes that his aim is:-

... to present a thorough investigation of the various systems of symbolic reasoning allied to ordinary algebra ... . The chief examples of such systems are Hamilton's Quaternions, Grassmann's Calculus of Extension, and Boole's Symbolic Algebra.

Also in the Preface Whitehead also gives his views on the nature on mathematics and the philosophy of mathematics:-

Mathematics in its widest signification is the development of all types of formal, necessary, deductive reasoning. The reasoning is formal in the sense that the meaning of propositions forms no part of the investigation. The sole concern of mathematics is the inference of proposition from proposition. ... The ideal of mathematics should be to erect a calculus to facilitate reasoning in connection with every providence of thought, or external experience, in which the succession of thoughts, or of events can be definitely ascertained and precisely stated. So that all serious thought which is not philosophy, or inductive reasoning, or imaginative literature, shall be mathematics developed by means of a calculus.

Although Whitehead became very productive after his marriage, he never considered himself a creator of new areas of mathematics, but rather as a developer of ideas introduced by others. This does not mean that his contribution should be considered any less important because of this but certainly Cambridge seems to have undervalued his contribution. In 1894 Whitehead became an examiner for the Mathematical Tripos. In 1903 he was promoted to Senior Lecturer, a position which had only just been established at Cambridge.

Whitehead is perhaps best known for his collaboration with Bertrand Russell. We shall give details of this collaboration below, but first we shall complete the details of Whitehead's career. He remained at Cambridge until 1910 but, in some sense, having not made the grade in mathematics and, having little prospects of a mathematics chair at Cambridge, he moved to the University of London. This explanation of his move is almost certainly basically correct and this indeed was the motivation behind Whitehead's thinking; on the face of it, however, rather different and dramatic events ended his association with Cambridge.

In 1910 Andrew Forsyth, who had been a close friend of Whitehead's since his student days, had a love affair with Marion Amelia Boys, the wife of C V Boys, and the scandal forced him to resign his chair at Cambridge. Whitehead did everything he could to ensure that Forsyth kept his Fellowship. The decision as to whether he could keep the Fellowship was taken by the Council of Trinity and Whitehead, as a member of that Council, argued strongly that Forsyth should be allowed to remain a Fellow of Trinity. Whitehead was outvoted on the Council, however, and shortly after this he resigned his Senior Lectureship and his Fellowship.

The Council then voted that Whitehead had served as a Lecturer for over 25 years (the maximum period) so must leave his post. Whitehead's appointment as Senior Lecturer still had three years to run but he did not stay to argue his case. He moved to London in the summer of 1910 with no job to go to. In 1914, after four years without a proper position, he became Professor of Applied Mathematics at the Imperial College of Science and Technology in London. He accepted a chair in philosophy at Harvard University in 1924, and he taught at Harvard until his retirement in 1937.

Bertrand Russell entered Cambridge in 1890 and immediately Whitehead, as examiner for the entrance examinations, spotted Russell's brilliance in his examination papers. Whitehead argued that Russell should be awarded a more prestigious scholarship than his marks would have merited and indeed this was agreed. When Russell was in his second year as an undergraduate he was taught by Whitehead. Their collaboration on Principia Mathematica appears to have begun near the end of 1900, although both men failed to remember the exact time their collaboration began when interviewed late in their lives. In fact they had attended the International Congress of Mathematicians in Paris in 1900 and there they had learnt about Peano's work on the foundations of mathematics. This led to them study Peano's papers and this must have been a major factor in getting their collaboration started.

At the time they began collaborating, Whitehead was working on his article Memoir on the algebra of symbolic logic while Russell was close to finishing the first draft of his Principles of mathematics. Whitehead was planning a second volume of Treatise on Universal Algebra but both their plans were somewhat disrupted in 1901 when Russell discovered his famous set theory paradox. After the initial worry over the paradox they joined forces on Volume 2 of Russell's work so, by 1903, Whitehead was working simultaneously on two different second volumes. Realising that this was not the optimal course for him he abandoned the second volume of his own work to concentrate on his collaboration with Russell. Their joint work attempted to construct the foundations of mathematics on a rigorous logical basis and it was carried out with Russell as the philosopher on the project and Whitehead as the mathematician.

Working with Russell did not occupy Whitehead completely for he continued to produce work of his own. In 1906 he published The axioms of projective geometry and, in the following year, The axioms of descriptive geometry. The first volume of Principia Mathematica was published in 1910, the second in 1912, and the third in 1913. He also wrote the popular mathematics book An introduction to mathematics which was published in 1911, between Volumes 1 and 2 of the Principia.

As the Principia Mathematica neared completion, Whitehead turned his attention to the philosophy of science. This interest arose out of the attempt to explain the relation of formal mathematical theories in physics to their basis in experience, and was sparked by the revolution brought on by Einstein's general theory of relativity. In The Principle of Relativity (1922), Whitehead presented an alternative to Einstein's views.

Science and the Modern World (1925), a series of lectures given in the United States, served as an introduction to his later metaphysics. Whitehead's most important book, Process and Reality (1929), took this theory to a level of even greater generality.

Whitehead received many honours throughout his career. Elected to the Royal Society in 1903, he was awarded the Society's Sylvester Medal in 1925 because of his work on the foundations of mathematics and his studies of physical concepts. The Royal Society of Edinburgh awarded him their James Scott Prize in 1922 (he was the first recipient). Columbia university awarded him their Butler Medal in 1930 and in the following year he was elected to the British Academy. He was awarded the Order of Merit in 1945. Many universities awarded him an honorary degree including Manchester, St Andrews, Wisconsin, Harvard, Yale and Montreal.

Article by:J J O'Connor and E F Robertson

October 2003

MacTutor History of Mathematics
[http://www-history.mcs.st-andrews.ac.uk/Biographies/Whitehead.html]